Soldato
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Running in a vacuum
- Thread starter jwest
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Soldato
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This is a nice question, and very similar to some of the research I am doing at the moment (I work on road bike aerodynamics).
As with any question that relates science to a real-world scenario, it can be made as complicated or as simple as we wish to make it, depending on which assumptions we choose to make, and or how much detail is required from an answer.
So the first simplification to make is to ignore anything to do with 'vacuum'. It complicates the problem, and is a bit irrelevant. The OP is asking what speed could be obtained if 100% of the energy output from the runner is converted to kinetic. The specific logistics surrounding this become irrelevant, since there are multiple theoretical ways to achieve this besides vacuum.
The article states that the total power output over the 100m was 81.58 kJ (which I'm a little skeptical about, but nevermind!). If we were talking about bikes, I could simply now throw that into the kinetic energy equation and give you a terminal velocity. But since running is such an inefficient form of travel, that's going to give us a massive over-estimate. We can incorporate that inefficiency into the equation though as follows though:
Energy output * efficiency = 0.5 * mass * velocity^2.
Rearranging ...
Velocity = Sqrt(Energy output * efficiency / (0.5 * mass))
With the assumption that our mass is about 85kg, and energy is as given, that gives a terminal velocity of:
Velocity = 43.81 * sqrt(efficiency) ... metres per second
or..
96 * sqrt(efficiency) ... miles per hour
In other words, if Usain Bolt were a cyclist, sprinting in a drag-less, loss-less environment, he would hit a velocity of 96mph assuming the power output as given. I did have a book somewhere that compared the efficiencies of different means of human-powered transport; alas I can't find it. But if someone knows an appropriate value for the efficiency of running, drop it in the formula above and you'll have your answer.
For the sake of the OP, assuming running is 30% efficient (absolute guesstimate), that gives us a top speed for Usain of 52.6mph
As with any question that relates science to a real-world scenario, it can be made as complicated or as simple as we wish to make it, depending on which assumptions we choose to make, and or how much detail is required from an answer.
So the first simplification to make is to ignore anything to do with 'vacuum'. It complicates the problem, and is a bit irrelevant. The OP is asking what speed could be obtained if 100% of the energy output from the runner is converted to kinetic. The specific logistics surrounding this become irrelevant, since there are multiple theoretical ways to achieve this besides vacuum.
The article states that the total power output over the 100m was 81.58 kJ (which I'm a little skeptical about, but nevermind!). If we were talking about bikes, I could simply now throw that into the kinetic energy equation and give you a terminal velocity. But since running is such an inefficient form of travel, that's going to give us a massive over-estimate. We can incorporate that inefficiency into the equation though as follows though:
Energy output * efficiency = 0.5 * mass * velocity^2.
Rearranging ...
Velocity = Sqrt(Energy output * efficiency / (0.5 * mass))
With the assumption that our mass is about 85kg, and energy is as given, that gives a terminal velocity of:
Velocity = 43.81 * sqrt(efficiency) ... metres per second
or..
96 * sqrt(efficiency) ... miles per hour
In other words, if Usain Bolt were a cyclist, sprinting in a drag-less, loss-less environment, he would hit a velocity of 96mph assuming the power output as given. I did have a book somewhere that compared the efficiencies of different means of human-powered transport; alas I can't find it. But if someone knows an appropriate value for the efficiency of running, drop it in the formula above and you'll have your answer.
For the sake of the OP, assuming running is 30% efficient (absolute guesstimate), that gives us a top speed for Usain of 52.6mph
This is a nice question, and very similar to some of the research I am doing at the moment (I work on road bike aerodynamics).
As with any question that relates science to a real-world scenario, it can be made as complicated or as simple as we wish to make it, depending on which assumptions we choose to make, and or how much detail is required from an answer.
So the first simplification to make is to ignore anything to do with 'vacuum'. It complicates the problem, and is a bit irrelevant. The OP is asking what speed could be obtained if 100% of the energy output from the runner is converted to kinetic. The specific logistics surrounding this become irrelevant, since there are multiple theoretical ways to achieve this besides vacuum.
The article states that the total power output over the 100m was 81.58 kJ (which I'm a little skeptical about, but nevermind!). If we were talking about bikes, I could simply now throw that into the kinetic energy equation and give you a terminal velocity. But since running is such an inefficient form of travel, that's going to give us a massive over-estimate. We can incorporate that inefficiency into the equation though as follows though:
Energy output * efficiency = 0.5 * mass * velocity^2.
Rearranging ...
Velocity = Sqrt(Energy output * efficiency / (0.5 * mass))
With the assumption that our mass is about 85kg, and energy is as given, that gives a terminal velocity of:
Velocity = 43.81 * sqrt(efficiency) ... metres per second
or..
96 * sqrt(efficiency) ... miles per hour
In other words, if Usain Bolt were a cyclist, sprinting in a drag-less, loss-less environment, he would hit a velocity of 96mph assuming the power output as given. I did have a book somewhere that compared the efficiencies of different means of human-powered transport; alas I can't find it. But if someone knows an appropriate value for the efficiency of running, drop it in the formula above and you'll have your answer.
For the sake of the OP, assuming running is 30% efficient (absolute guesstimate), that gives us a top speed for Usain of 52.6mph
awsomeses
For an amusing and probably meaningless calculation, if we assume that Mr. Bolt produces a power P for a time T in order to cover a distance s, then his instantaneous speed v will be sqrt(2Pt/m) at time t where 0 <= t <=T, if all his power is converted into kinetic energy.
Integrating this with respect to t over the interval [0,T] gives us s=(2/3)*sqrt(2P/m)*T^(3/2).
If we google a few numbers (they're on the internet, so they must be true) for Mr Bolt we have m=94Kg and P=2.1KW (for his world record run). Plugging these in, if all Mr Bolt's power were converted to energy of motion we would get T=7.96 seconds.
Fire away chaps!
Integrating this with respect to t over the interval [0,T] gives us s=(2/3)*sqrt(2P/m)*T^(3/2).
If we google a few numbers (they're on the internet, so they must be true) for Mr Bolt we have m=94Kg and P=2.1KW (for his world record run). Plugging these in, if all Mr Bolt's power were converted to energy of motion we would get T=7.96 seconds.
Fire away chaps!
There is something very odd going on with those news articles and the stated powers (hence my skepticism above). It states a total energy output of 81kJ over the 100m. But that would give an average power output of ~8.5kW. ... way above the supposed 'peak' output of ~2kW. Am I missing something obvious???
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FNG Magnolia made me do a funny but you just won the thread. Maybe the whole forum*Calculations*
For the sake of the OP, assuming running is 30% efficient (absolute guesstimate), that gives us a top speed for Usain of 52.6mph
For the sake of the OP, assuming running is 30% efficient (absolute guesstimate), that gives us a top speed for Usain of 52.6mph
Your maths is faultless. Unfortunately, the human body has not evolved to cope with running at 52.6 mph. A person could simply not physically run at this speed. But hey, this is all hypothetical right ? So I guess there is a loch ness monster, a big foot and an alien in Area 51.
Your maths is faultless. Unfortunately, the human body has not evolved to cope with running at 52.6 mph. A person could simply not physically run at this speed. But hey, this is all hypothetical right ? So I guess there is a loch ness monster, a big foot and an alien in Area 51.
When were OCUK science questions anything but hypothetical?
The mystery has been solved:
http://fakescience.org/post/597833893/how-do-magnets-work
Obvious, really.
There's a big difference between "much faster" (the argument made) and "faster" (the argument you have just countered).
An athlete will run faster with a significant tailwind. The Olympics has a wind limit because it will make enough difference to be relevant in races timed to 1/1000th of a second. It could be considered "much faster" in that context, where 0.1s is a big difference, but it wouldn't be considered "much faster" in day to day terms. Maybe 30mph instead of 28mph.
So I think that Zefan has a good point when he counters the assumption implicit in the OP (that without air resistance a sprinter would be able to convert 12.5 times as much energy into motion) by arguing that if that was the case then a tailwind would have a much larger effect than it actually does.
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Surely this could be roughly tested on a treadmill?
Or take the max speed of usain bolt, get him to do the 100m sprint with a tailwind at this speed. If he is running at the same speed as the wind then he wouldn't be running into the wind and thus have very little wind resistance?
*has no fancy formula to compete with above
*
Or take the max speed of usain bolt, get him to do the 100m sprint with a tailwind at this speed. If he is running at the same speed as the wind then he wouldn't be running into the wind and thus have very little wind resistance?
*has no fancy formula to compete with above
*
My god. I wrote almost that exact reply earlier(although I was quite overly aggressive), but I decided it would've been a bad idea to post it, thanks!